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John Horton Conway

cinelli
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John Horton Conway

#311214

Postby cinelli » May 22nd, 2020, 9:07 pm

This is not a puzzle, but this board seems the most appropriate place for an obituary.

Who was the most famous mathematician of the twentieth century? Arguably it was the eccentric John Horton Conway, who has recently died. Siobhan Roberts wrote a long appreciation of him in the Guardian and she has also written a book about him:

https://www.theguardian.com/science/201 ... -the-world

He was remembered too in Radio 4’s obituary programme “Last Word”:

https://www.bbc.co.uk/sounds/play/m000j2vm

Probably Conway reached popular recognition by inventing the Game of Life.

Cinelli

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Re: John Horton Conway

#311370

Postby UncleEbenezer » May 23rd, 2020, 12:00 pm

Hmmm, is that worth a thwack or a rec?

I knew him at Cambridge, where he made a huge impression from the start. Later as a postgrad I was privileged to meet him socially, and play various games against him and others of his inner circle. I posted a reminiscence/obit with a few anecdotes from that time on April 14th.

Not sure about superlative claims though. From the same generation, Hawking was surely more famous (another presence from my Cambridge days, though not someone I ever knew other than to stand respectfully aside to let his wheelchair and helpers pass).. In recreational maths, Martin Gardner was his friend. Earlier in the 20th century was the era of Hardy ("Apology"), Littlewood and Ramanujan ("Knew Infinity"), not to mention Russell. And the most famous to end his career at Princeton - Einstein.

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Re: John Horton Conway

#311440

Postby GoSeigen » May 23rd, 2020, 2:50 pm

UncleEbenezer wrote:Hmmm, is that worth a thwack or a rec?

I knew him at Cambridge, where he made a huge impression from the start. Later as a postgrad I was privileged to meet him socially, and play various games against him and others of his inner circle. I posted a reminiscence/obit with a few anecdotes from that time on April 14th.


Ha! Had no idea Game of Life came out of Go, but makes perfect sense now that I know it. Was he any good as a player?

I was lucky enough to study under a couple of Japanese Sensei and reached 2nd dan within about 2 years. Haven't played since I was last in Japan in 2017. No Japanese ever mentioned game of Life to me...


GS

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Re: John Horton Conway

#311545

Postby 9873210 » May 23rd, 2020, 6:21 pm

In deference to Conway's wishes we should be remembering him for things like the surreal numbers rather than the game of life.

The surreal numbers include the real numbers and are constructed using set theory rather than adding a "completion" axiom to the rationals. They also include rigorously concepts of the infinite and infinitesimal.

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Re: John Horton Conway

#311585

Postby Gengulphus » May 23rd, 2020, 7:46 pm

cinelli wrote:This is not a puzzle, but this board seems the most appropriate place for an obituary.

Who was the most famous mathematician of the twentieth century? Arguably it was the eccentric John Horton Conway, who has recently died. Siobhan Roberts wrote a long appreciation of him in the Guardian and she has also written a book about him:

https://www.theguardian.com/science/201 ... -the-world

He was remembered too in Radio 4’s obituary programme “Last Word”:

https://www.bbc.co.uk/sounds/play/m000j2vm

Another good obituary is this one in Scientific American: https://blogs.scientificamerican.com/ob ... hn-conway/

Like UncleEbenezer, I knew him at Cambridge, first as a lecturer as an undergraduate, and later more socially as a postgraduate. I played many games of backgammon (probably rather too many!) either against him or with him looking on and probably kibitzing... (This was not ill-mannered, by the way: kibitzing was an expected accompaniment to playing backgammon in the maths department common room!)

I think there's a more arguable case that he was the most famous pure mathematician of the 20th century; as UncleEbenezer says, Einstein and Hawking were surely more famous, but they were primarily applied mathematicians / theoretical physicists (I won't try to commit myself as to which - the distinction between them is decidedly hard to pin down!).

GoSeigen wrote:Ha! Had no idea Game of Life came out of Go, but makes perfect sense now that I know it. Was he any good as a player?

I suspect it only came out of Go in the sense that a Go set is a convenient tool to investigate Life patterns if you have to do that without a computer: the board is a big enough square grid to hold a good variety of interesting Life patterns, and the black and white stones can help keep track of the states of the individual cells (though having three colours rather than just two would make it easier). There's no similarity of rules between them, so I don't think the Game of Life was derived from Go.

I never saw him play Go, so have no idea how good he was as a player. I'd be very surprised though if he wasn't a player at least at some stage in his life - it would be totally out of character for him not to have investigated the game! Also, he invented a decidedly challenging game called "Philosopher's Football" or "Phutball" for short that can be played using a Go board and stones (though properly speaking one should block off four columns to reduce it to a 19x15 board). Again, it has very different rules - from both Go and the Game of Life.

His 'surreal numbers' are a very rich number system - one in which infinity, infinity+1, infinity-1, infinity squared, the square root of infinity, etc all exist, are all infinite and are all different from each other, 1/infinity, 1/(infinity+1), 1/(infinity-1), etc, all exist, are all infinitesimal and are all different from each other, etc, etc, etc. This doesn't contradict the mathematical rule infinity+1 = infinity that people tend to learn, because that rule applies to the cardinal numbers - which are useful for counting how many there are of something. The surreal numbers are instead useful for measuring how far ahead you are in a class of games, and can be used in the analysis of how far ahead you are in a larger class of games. They are for instance useful in analysing Go endgames.

He did an amazing variety of things in a very wide range of mathematical areas, from very deep stuff that I won't try to describe because I don't really understand it myself to ingenious 'tricks'. An example of the latter is his 'Doomsday rule' for quickly mentally calculating the day of the week for any calendar date. I won't try to describe it fully - see the link for that - but a very simple version of it for any date in the current year is:

* Memorise once and for all the following collection of 'Doomsdays':

Duplicated even numbers from 4 upwards: 4/4, 6/6, 8/8, 10/10, 12/12
The 5-9 pair: 9/5, 5/9
The 7-11 pair: 11/7, 7/11
The last day of February - i.e. the 28th in non-leap years, the 29th in leap years
The 3rd of January in non-leap years, the 4th of January in leap years (mnemonic "3 non-leap years, the 4th is a leap year")

Note that in the first three categories, it doesn't matter whether you use English or American date numbering, as you end up memorising the same collection of Doomsdays either way.

* At the start of each year, look up the day of the week of one of those 'Doomsdays' and memorise it for the year. For example, this year's Doomsdays are Saturdays.

* When given a date in the current year, find the Doomsday in the month it specifies, which always exists except when the month is March: in that case, use the last day of February and think of it as the 0th of March. Then do a subtraction to work out how many days it is ahead of or behind the Doomsday. Divide by 7 to work out how many full weeks and odd days that is, and use the odd days to work out the day of the week from the Doomsday.

For example, Christmas Day this year is a Friday, because the December Doomsday is 12/12, 25-12 = 13 days ahead, which is a full week and 6 odd days ahead; 6 days ahead from Saturday is Friday.

With a bit of practice and a little facility at mental arithmetic, it's not difficult to get one's time for doing that calculation down to a second or two, and one can expand the range of years covered a bit by remembering e.g. that last year's Doomsdays were Thursdays and next year's will be Sundays. Covering a lot of years involves learning another calculation to get a year's Doomsday day of the week, and if one wants to do the job really well, two versions of that calculation, one for the Julian calendar and one for the Gregorian calendar, plus memorising a whole lot of dates when different countries switched from the former to the latter - much more challenging!

No deep mathematics in the Doomsday rule, of course - just imagining that there might be an easily memorable collection of dates that all fall on the same day of the week in each year and cover all the calendar months, and then actually looking for them and finding them. But quite an impressive trick to those who don't know how it's done, and even to those who do for doing all years as opposed to just the current year and maybe a small range of years around it!

Gengulphus

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Re: John Horton Conway

#311592

Postby UncleEbenezer » May 23rd, 2020, 8:14 pm

Yes, backgammon and kibitzing are fond memories. I must've played you if our times there overlapped! If I repost what I wrote, you'll have the advantage of me, knowing whether our times there did coincide.

The maths he seemed most involved with in my time was groups, including the Monster. Mind you, that may have been of its time: the world and his dog were mad about a recreational group (albeit a smaller and simpler one) around then ...

https://bahumbug.wordpress.com/2020/04/14/end-of-life/ wrote:RIP John Conway.

We’ve lost not just a great man, but a formative influence on my youth. Conway was one of my strongest and indeed fondest memories from my Cambridge days. Most famous for a light entertainment, the “game of life”. Now it seems a casualty of the coronavirus.

My first recollection of him goes right back to late July (I think) 1979, between the end of school a few weeks earlier and going up to Cambridge as a student that autumn. We (future students) were invited up to Cambridge for a two-week pre-course giving us a flavour of the student life, with lectures and a whole lot of socialising, and most importantly (at least to me) freeing us of the vague dread that came from leaving the familiar (school and home) and taking a leap into the unknown.

Conway was not one of the main lecturers on that pre-course, but the single lecture he gave was certainly a highlight. Ever the showman, in this context he was as much a fine stand-up comedian as great mathematician! When he used his sock to rub out the blackboard, it kind-of helped me towards discarding the wretched things from my life. His scruffy hair and beard (see anecdote below) are also attributes I’ve adopted.

A prop to that lecture was a magic cube, which he offered to audience members to try before demonstrating solving it. I didn’t get my hands on it at the time, but I did subsequently manage to source one in the autumn term, when it became a practical exercise in Group Theory (a first-term lecture course, under a different lecturer). About a year or so later that magic cube started to appear in the shops, and became madly popular under the name Rubik’s Cube.

I didn’t have any significant contact with Conway during my undergraduate years, but I did get to know him somewhat as a graduate student, when the doors to the DPMMS common room and one or two other venues opened to me. As one of the leading lights of games there – from Backgammon (which at DPMMS was played like nowhere else) to the fiendish Phutball – he might almost have been a Bad Influence, though in a Good Way. It was there that I observed his acolytes (including another somewhat-famous mathematician Simon Norton), and thought that too many of them were depressed and depressing people with no life. I could also see that being my future if I remained in academia without at least a break, and it was on the basis of that that I made the decision that I would leave it and face the real world (at least for a while) after finishing Part III.

My final Conway anecdote comes from my last weeks in Cambridge in summer 1983. I was walking down Kings Parade with my then-girlfriend (the woman I still really regret having split up with after all these years), and exchanged a wave with Conway as he passed in the other direction. Once we were past, my girlfriend wondered why I had waved to that tramp! Just to be clear, she was just expressing surprise, not disapproval or any such negative thing.

Requiescat in Pace.

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Re: John Horton Conway

#311596

Postby mc2fool » May 23rd, 2020, 8:21 pm

Gengulphus wrote:
GoSeigen wrote:Ha! Had no idea Game of Life came out of Go, but makes perfect sense now that I know it. Was he any good as a player?

I suspect it only came out of Go in the sense that a Go set is a convenient tool to investigate Life patterns if you have to do that without a computer: the board is a big enough square grid to hold a good variety of interesting Life patterns, and the black and white stones can help keep track of the states of the individual cells (though having three colours rather than just two would make it easier). There's no similarity of rules between them, so I don't think the Game of Life was derived from Go.

I'd never heard so, and I used to know a guy by the name of John Francis who was one of Conway's students and claimed to be the first to ever program up Life. The way he told it he found Conway one day trying out patterns on lots of adjacent chess boards* spread out over the floor and thought "that's silly" and went off and coded it up on the college's computer, and inevitably managed to prove something to Conway that he'd been experimenting with that would have taken him yonks to do on the chess boards.

(* I'm pretty sure John said chess boards but it was over 40 years ago he told me the story ... ;))

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Re: John Horton Conway

#311598

Postby Lootman » May 23rd, 2020, 8:32 pm

UncleEbenezer wrote:Yes, backgammon and kibitzing are fond memories.

Kibitzing is also known in the chess world, despite the fact that the game should be played in silence. At least for casual play it is not unusual for observers to pass critical commentary whilst the two players trash talk each other. I've seen it in bridge as well.

Since we are all name-dropping, I played chess against the grandmaster Ray Keene at Cambridge a few times. Needless to say I lost every time. He was always very gracious and took the time afterwards to explain exactly why I had lost.

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Re: John Horton Conway

#312015

Postby cinelli » May 25th, 2020, 12:01 pm

Thank you for the extra reminiscences about Prof Conway. I came to him from Martin Gardner’s Scientific American columns and I have also enjoyed making a Conway cube (cf). I have just watched an interview between him and his biographer Siobhan Roberts. As 9873210 has pointed out, it seems I have committed the sin of describing him as “Conway, the inventor of the game of life”. He would like to be remembered more as the creator of surreal numbers.

Cinelli

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Re: John Horton Conway

#314018

Postby stewamax » May 31st, 2020, 6:59 pm

In Conway's time, the Cambridge Maths Lab in Corn Exchange Street had what was probably the world's first distributed CAD system - a PDP7 with a round screen - linked to the mainframe Titan. Many people wanted time on this wondrous invention but it was so ideal for playing Life that I would guess John Conway (same Department - different building) was persuasive enough to filch sessions. Since Titan had a proper time-sharing system with (for its time) an extraordinary number of teletypewriter terminals - at least twenty in the main terminal room alone and with others sited remotely - Conway could have programmed from the Maths Dept and come over only to play.

I remember after working in the Lab very late one night, I called in the machine room to say goodnight to the operators and found it in darkness. Since Titan had very human responses to errors and questions, it was my first encounter with a machine that was passing the Turing test!

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Re: John Horton Conway

#314035

Postby stewamax » May 31st, 2020, 8:20 pm

CP Snow - who contributed to GH Hardy's A Mathematician's Apology mentions there that Hardy once commented that he was for a time "the fifth best pure mathematician in the world". I don't think he ever said who was the best.
My vote for the best poly-mathematician of the 20th C would be John von Neumann - as the successor to the late 19th C Poincare who also was master of umpteen different fields.

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Re: John Horton Conway

#314075

Postby UncleEbenezer » June 1st, 2020, 1:45 am

stewamax wrote:CP Snow - who contributed to GH Hardy's A Mathematician's Apology mentions there that Hardy once commented that he was for a time "the fifth best pure mathematician in the world". I don't think he ever said who was the best.

Specifically, Snow wrote a long foreword to the Apology, though I don't recollect it from when I first read the Apology. Indeed, the Apology was one of the main influences that persuaded me to go and study Maths at Cambridge, though of course the world of Snow and Hardy was long-gone. Though come to think of it, it was the precisely the ending of that world that opened Cambridge to plebs like me with no Latin!

Hardy and Littlewood would each, if asked, rate the other as the greater mathematician. That kind of elitist modesty was kind-of an integral part of their world. And then of course there was Hardy's genius protégé Ramanujan, of the extraordinary life story.

As for Von Neumann - Conways's chair at Princeton was of course named after him 8-)

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Re: John Horton Conway

#314120

Postby stewamax » June 1st, 2020, 9:26 am

UncleEbenezer wrote:Indeed, the Apology was one of the main influences that persuaded me to go and study Maths at Cambridge, though of course the world of Snow and Hardy was long-gone.

Nahhh .... you were (like Hardy) seduced by the future port and walnuts after dinner in the SCR after you obtained your Fellowship, although as things turned out, Hardy was lukewarm about them in practice, although Littlewood was more congenial.

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Re: John Horton Conway

#371941

Postby Gengulphus » January 1st, 2021, 10:34 am

Another link I've recently encountered, this one to an article about Conway's "best known (and, to him, least favorite) creation":

https://www.nytimes.com/2020/12/28/scie ... -life.html

Gengulphus

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Re: John Horton Conway

#632672

Postby GrahamPlatt » December 8th, 2023, 7:22 pm

“ At the turn of the millennium, only twelve oscillator periods remained to be found in Conway's Game of Life. The search has finally ended, with the discovery of oscillators having the final two periods, 19 and 41, proving that Life is omniperiodic.”

https://arxiv.org/abs/2312.02799

This seemed to be the most appropriate place to post.

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Re: John Horton Conway

#634155

Postby NomoneyNohoney » December 15th, 2023, 1:26 pm

Thoroughly enjoyed these posts, about subjects and people of which and whom I know absolutely nothing.
Sometimes I marvel at people's erudition and wisdom.


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